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Just 23% of Americans say they are at least somewhat worried about Zika

This is after the CDC sent out a travel warning for a Florida neighborhood

Washington (CNN)A new poll finds most Americans aren't worried about someone in their family contracting a case of Zika, even as a growing number of mosquito-borne cases of the disease in a Florida neighborhood prompted a historic travel warning from the Centers for Disease Control.

Overall, just 23% in the CNN/ORC Poll say they are at least somewhat worried about themselves or a family member becoming a victim of the virus, while 77% say that's not a very big concern.

That's less than the share saying that they were worried about contracting the Ebola virus in fall of 2014 (27% were at least somewhat worried about that). Nearly half of all adults say they are "not at all worried" about Zika, well above the 39% who were unfazed by Ebola.

The CNN/ORC Poll on this topic was conducted Friday through Sunday, after the announcement that four cases in Florida were the first in the US that were locally transmitted via mosquitoes, but before the CDC issued its warning about travel to the area where the infections were found.

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Women express slightly more concern about the Zika virus than men -- 27% of women are at least somewhat worried, vs. 19% of men. And despite the implications for pregnant women, younger women are no more concerned than older ones. Southerners are more likely than others to have any concern about it, just 37% say they are not at all worried about Zika, compared with majorities in the West (55%) and Midwest (57%) and 43% in the Northeast.

Most Americans are at least somewhat confident in the federal government's ability to prevent an epidemic of the Zika virus from occurring in the US, but that's below the level who were confident that the government could keep Ebola from turning into a nationwide epidemic. In fall 2014, 71% said they were somewhat or very confident in the government's ability to prevent an outbreak, that stands at 62% when considering Zika now. Democrats are more confident that the government can halt the spread of Zika than Republicans (71% among Democrats vs. 62% among Republicans).

And considering the upcoming Olympic Summer Games, set to kick off this week in Rio de Janeiro, Americans are more worried about the threat of terrorism at the upcoming Olympic Games than they are about the risk of Zika for athletes traveling to Brazil, which is facing an epidemic of the virus.

A majority of 57% say a terrorist attack is at least somewhat likely at the Olympics, on par with the 57% who were that worried about an attack in Sochi, Russia, during the Olympic Winter Games held there in 2014. Notably, not even the Olympics are immune from political divides, with Republicans far more apt to express concern about a terror attack than Democrats, 65% among Republicans vs. 46% among Democrats.

Less than half overall, 47%, say an outbreak of the Zika virus among athletes competing in the games is at least somewhat likely. The poll finds few meaningful demographic or political differences on that score.

Several prominent athletes have opted out of this year's games, some on account of the Zika epidemic, but most Americans say those withdrawals from competition make little difference in their plans to watch the games. More than 8-in-10 (84%) say it hasn't changed their interest in the games, while just 11% say they are now less interested in the Olympics than they were before, 5% are more interested.

Overall, 54% of Americans plan to watch some or a lot of the upcoming Olympics, 46% very little or none at all. That's about the same as the share who planned to watch the Olympic Winter Games in Sochi in 2014, according to a survey at the time from the Pew Research Center.

The CNN/ORC Poll was conducted by telephone July 29-31 among a random national sample of 1,003 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points.